In oil exploration and production, the saturations and wettability of the rock/fluid system are major factors controlling the location, flow, and distribution of immiscible fluid phases in a reservoir. Saturations are relative measures of the fluid content in the formation pore space and, in the case of irreducible saturations, of the immobile or trapped fluid content. Together with wettability, saturations and irreducible saturations will determine the mobile and hence producible oil content of a reservoir.
In a porous medium of uniform wettability containing at least two immiscible fluids one of them is defined as the wetting fluid. At equilibrium, the wetting fluid occupies completely the smallest pores and is in contact with a majority of the rock surface (assuming, of course, that the saturation of the wetting fluid is sufficiently high). The non-wetting fluid occupies the center of the larger pores and form globules that extend over several pores.
The wettability of a three phase system of solid surface (s), oil (o) and water (w) is typically measured through the contact angle cos θ, which results from the equilibrium condition for the surface tensions at a point where the three phases meet:γso−γsw−γow cos θ=0,  [1]where the surface tensions γ have subscripts referring to the respective two phases forming the interface.
Methods of measuring wettability are described for example in the U.S. Pat. No. 7,532,983 to B. Montaron.
At the present state of art, macroscopic manifestation of wettability are used in the form of capillary pressure curve and relative permeability for the purpose of determining or simulating the production performance of a reservoir. Examples of such uses of the derivatives of wettability are described in the published United States Patent Application 2007/0276639 A and other published sources. Explicit maps of fields of a wettability parameter are therefore typically not included into reservoir simulations as the dependence of fluid movement on wettability is implicit and arises out of capillary pressure and relative permeability. Therefore it should be understood that, depending on the context, reference to wettability in this description may include reference to such closely related parameters. In general the industry is currently more concerned with developing databases linking core capillary pressure and relative permeability measurements at various wettability states to rock types. The latter are often characterized by a standard wettability index (Amott, Amott-Harvey, USBM) instead of contact angles. However the various indices and contact angle are equivalent.
The so-called wettability index measurements on cores can be used to map the patterns of rock wettability variation across the reservoir and by rock type. Given the wettability index and rock type at any point in the reservoir, a set of capillary pressure Pc and relative permeability curves Kr can be assigned in a reservoir simulator such as Schlumberger's Eclipse™ for every spatial location using for example an average Pc calculated by
                              P          c                =                                            γ              ow                        ⁢            cos            ⁢                                                  ⁢            θ                                2            ⁢            π            ⁢                                                  ⁢            r                                              [        2        ]            where r represents an effective capillary or pore radius for the formation.
Given the generally very sparse availability of detailed core analysis measurements however, sets of Pc and Kr curves are more often assigned solely by rock type with little regard to the variation of wettability across the reservoir for the same rock type.
It is further known to determine the electrical resistivity of geologic formations surrounding and between boreholes drilled into the geologic formations of interest, with electro-magnetic (EM) measurements from the surface, including the sea bottom, from surface-to-borehole, and/or between boreholes (crosswell EM).
In two articles, “Crosshole electromagnetic tomography: A new technology for oil field characterization”, The Leading Edge, March 1995, by Wilt et al. and “Crosshole electromagnetic tomography: System design considerations and field results”, Society of Exploration Geophysics, Vol. 60, No. 3, 1995 by Wilt et al., the authors describe the principles guiding the measurement of geologic formation resistivity with low frequency EM systems.
Methods and tools for performing EM measurements are further described in a number of patents and patent applications including the co-owned U.S. Pat. No. 6,393,363 to Wilt and Nichols.
In “Using Crosswell Electromagnetic to Map Water Saturation and Formation Structure at Lost Hills”. SPE Western Regional Meeting, 26-30 Mar. 2001, Bakersfield, Calif. (SPE paper 68802) by M. Wilt et al., the authors describe a qualitative method of estimating the change in water saturation from time-lapse cross-well EM data.
The published international patent application WO2001/020366 provides further background related to reservoir resistivity mapping with deep electromagnetic measurement. It also teaches the combination or joint inversion of resistivity depth images with other geological and geophysical data to estimate the reservoir properties. The co-owned U.S. Pat. No. 7,363,164 to Little and LaVigne describes Archie and Waxman-Smits laws in the context of using dual and triple water models to interpret electrical resistivity measurements.
In view of the known art, it is seen as one object of the present invention to provide a new method of determining saturations, wettability or combined saturation and wettability maps covering the formation at a distance from the immediate vicinity of a borehole. More specifically, it is seen as an object of the invention to provide a method of extrapolating measurements into the space between two or more boreholes to determine saturations and/or wettability or related parameters at locations not accessible for direct measurements of such parameters.